基于伪四维投射坐标的多基链标量乘法

doi:10.11959/j.issn.1000-436x.2018078

Abstract

Abstract:

In order to address the problem of elliptic curve cryptosystem (ECC) for the expensive cost in scalar multiplication and the vulnerability to the power analysis attacks,a pseudo 4D projective coordinate-based multi-base scalar multiplication was proposed to optimize group operation layer and scalar multiplication operation layer,which aimed at increasing the performance of ECC and resisting common power analysis attacks.Experimental results show that compared with the state-of-the-art algorithms,the proposed algorithm decreases 5.71% of point doubling cost,3.17% of point tripling cost,and 8.74% of point quintupling cost under discrete group operations.When the key length is 160 bit,the proposed algorithm decreases 36.32% of point tripling cost,17.42% of point quintupling cost,and 8.70% of the system cost under continuous group operations.The analyzing of power consumption wave shows that the proposed algorithm can resist SPA and DPA attack.

Key words: elliptic curve cryptosystem, coordinate transformation, multi-base scalar multiplication, power analysis attack

CLC Number:

TP393

Ming XU,Liang SHI. Pseudo 4D projective coordinate-based multi-base scalar multiplication[J]. Journal on Communications, 2018, 39(5): 74-84.

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References 25

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密钥位数/bit	c₁	c₂	c₃	最短链长/个
160	0.223	0.321	0.254	30.621
192	0.238	0.363	0.432	54.682
256	0.415	0.502	0.347	62.644
384	0.323	0.452	0.328	91.097

算法	倍点	三倍点	五倍点
文献[14]	4M+6S	10M+6S	15M+10S
文献[15]	6M+2S	N/A	N/A
文献[17]	4M+4S	N/A	N/A
文献[19]	1M+8S	5M+10S	N/A
文献[20]	4M+6S	10M+6S	12M+13S
文献[21]	1I+2M+S	1I+7M+4S	1I+13M+5S
本文	3M+5S	7M+7S	11M+12S

算法	群运算方法	标量乘方法	总开销/次
文献[14]	雅可比	D＆A方法	1 950.60
文献[13]	雅可比	蒙哥马利阶梯	1 682.40
文献[17]	雅可比	多基链(2、3、5为基)	1 567.78
文献[16]	雅可比	双基链(2、3为基)	1 524.42
文献[15]	投射	蒙哥马利阶梯	1 396.20
文献[18]	仿射	多基链(1/2、3、5为基)	1 343.72
本文	伪四维	多基链(2、3、5为基)	1 236.16

Pseudo 4D projective coordinate-based multi-base scalar multiplication

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